Bayesian symbolic regression automates model discovery from data.
problem Learning closed-form mathematical models from data using heuristic methods.
method Probabilistic approach to symbolic regression, connecting to information theory and statistical physics.
result Probabilistic approach provides model plausibility and performance guarantees.
Study compares symbolic and distributional methods for relational learning.
problem Comparing symbolic and distributional paradigms for relational learning.
method Comparison of representation learning and relational learning on various tasks.
result Preliminary results suggest possible indicators for choosing between approaches.
Paper closes neural-symbolic learning loop with grammar model and back-search algorithm.
problem Slow convergence in neural-symbolic learning due to error propagation issues.
method Introduces grammar model as symbolic prior and back-search algorithm for efficient error propagation.
result Significantly outperforms RL methods in performance, converging speed, and data efficiency.
Bayesian symbolic regression uncovers missing physics from data with uncertainty quantification.
problem Incomplete knowledge of physical laws from experimental data.
method Bayesian symbolic regression using Reversible Jump Markov Chain Monte Carlo.
result Uncertainty quantification in recovered model structures.
VaSST uses soft symbolic trees for probabilistic symbolic regression.
problem Efficiently recover symbolic expressions from noisy data.
method Variational inference with soft symbolic trees.
result Superior performance in structural recovery and predictive accuracy.
Paper proposes a bijective approach for signal/symbol translation using variational auto-encoders.
problem Extracting symbolic information from signals, especially in music, is challenging and non-generic.
method Turned into a density estimation task, using two variational auto-encoders with additive constraint.
result Bijective signal/symbol translation achieved, allowing both signal-to-symbol and symbol-to-signal inference.
Meta-learning symbolic default hyperparameters from dataset properties.
problem Empirical hyperparameter optimization is slow and requires manual configuration.
method Evolutionary algorithm to learn symbolic hyperparameter formulas from dataset properties.
result Meta-learning finds viable symbolic defaults for ML algorithms.
Improves neural network search in combinatorial spaces of mathematical symbols.
problem Early commitment and initialization bias limit exploration in neural network search.
method Entropy regularization and distribution initialization methods.
result Improves performance, increases sample efficiency, lowers solution complexity.
New SDA models for big data analysis using aggregated symbols.
problem Handling large and complex datasets efficiently.
method Developing likelihood functions for symbolic data based on underlying measurement-level data.
result Efficient analysis of big data through reduced distributional summaries.
Neural-symbolic model improves link prediction in knowledge graphs.
problem Effective relational learning and reasoning for AI systems.
method Neural-symbolic graph neural network that learns over all paths in knowledge graphs.
result Neural-symbolic model outperforms path-based approaches in link prediction.
Symbolic regression finds simple formulas for implied volatility.
problem Discovering accurate parametric representations for implied volatility.
method Symbolic regression to find analytic formulas from market data.
result Symbolic regression identifies compact parametrizations with competitive fitting performance.
Perceptor Gradients learns symbolic representations from raw data.
problem Learning transferable symbolic representations from raw data.
method Decomposes policy into perceptor network and task encoding program.
result Efficiently learns symbolic representations for control tasks.
Symbolic LSTM improves time series forecasting by reducing hyperparameter sensitivity.
problem High sensitivity to hyperparameters and random initialization in numerical time series forecasting.
method Combining LSTM with a dimension-reducing symbolic representation.
result Symbolic representation alleviates forecasting problems and speeds up training.
Unified approach to structured prediction combining entropy regularization and neuro-symbolic logic.
problem Structured prediction challenges due to large output spaces and insufficient labeled data.
method Neuro-symbolic entropy regularization loss that restricts entropy regularization to valid structures.
result Models predict more accurately and are more likely to be valid.
NeSS combines neural and symbolic approaches for better compositional generalization.
problem Lack of compositional generalization in deep learning models.
method NeSS uses a neural network to generate traces, executed by a symbolic stack machine with sequence manipulation.
result Achieves 100% generalization performance across multiple domains.
Combines symbolic and raw audio models for structured, realistic-sound music generation.
problem Lack of long-range dependencies in raw audio models and unstructured music.
method Uses a Long Short Term Memory network for melodic structure and WaveNet for raw audio generation with symbolic conditioning.
result Creates structured, realistic-sounding compositions using both symbolic and raw audio models.
Extract symbolic models from deep learning with inductive biases.
problem Interpreting and discovering physical principles from deep neural networks.
method Introduce strong inductive biases in GNNs, encourage sparse latent representations, apply symbolic regression.
result Extracted symbolic equations from neural networks, including known force laws and new analytic formulas.
In this study we introduce a new technique for symbolic regression that guarantees global optimality. This is achieved by formulating a mixed integer non-linear program (MINLP) whose solution is a symbolic mathematical expression of minimum complexity that explains the observations. We demonstrate our approach by redis…
Symbolic regression improved by incorporating prior knowledge.
problem Insufficient guidance from training data alone for model accuracy.
method Multi-objective symbolic regression combining training data and prior constraints.
result Models that fit training data well and comply with prior knowledge.
Graph networks learn symbolic physics laws from simulations.
problem Learning interpretable physics laws from simulations.
method Inductive biases on graph networks for symbolic regression.
result Graph networks can learn symbolic laws of physics.
Paper applies GANs to symbolic music genre transfer.
problem Symbolic music genre transfer using GANs.
method CycleGAN architecture with additional discriminators to preserve structure.
result Fidelity of transformed music improved with additional discriminators.
SGE learns symbolic node representations from relational data.
problem Mining insights from complex, real-world systems.
method SGE uses frequent pattern mining on a node's neighborhood to learn symbolic node representations.
result SGE outperforms shallow node embedding methods on a venue classification task.
Representation learning has become an invaluable approach for learning from symbolic data such as text and graphs. However, while complex symbolic datasets often exhibit a latent hierarchical structure, state-of-the-art methods typically learn embeddings in Euclidean vector spaces, which do not account for this propert…
Secure Multiparty Computation protects data privacy in Symbolic Regression.
problem Data privacy in Symbolic Regression models.
method Secure Multiparty Computation for vertical partitioning.
result Comparable performance to centralized model while preserving privacy.
Study develops supervised algorithm for symbolic music style translation.
problem Transforming musical style while maintaining original content.
method Synthetic data generation for aligned training data, encoder-decoder model.
result Trained models produce meaningful accompaniments for real MIDI recordings.
Deep neural network generates symbolic equations from data.
problem Lack of insight into underlying mappings from traditional deep learning.
method Combines deep learning flexibility with symbolic solutions.
result Accurately generates governing equations for dynamical systems.
EPSTE: A geometric token and deep learning approach to estimating transfer entropy in neuroimaging time series
problem Inferring directed interactions between neural systems from EEG and MEG
method Reframing TE estimation as a learnable problem operating on structured symbolic representations
result EPSTE achieves near-perfect recovery of ground-truth directed structure and significantly lower absolute error than the baseline
Data-driven symbol detection improves performance in complex channels.
problem Designing robust symbol detectors in systems with poorly understood channels.
method Hybrid approach combining model-based algorithms with machine learning.
result Near-optimal performance of model-based algorithms achieved without channel model knowledge.
New IT representation improves symbolic regression approximations.
problem Finding better approximations to real-world data sets.
method Evolutionary Algorithm with IT representation using only mutation.
result IT representation finds better approximations than traditional methods.
Develops a Bayesian framework for symbolic regression of scientific expressions.
problem Lack of principled uncertainty quantification and interpretability in existing symbolic regression methods.
method Hierarchical Bayesian framework with tree-structured symbolic expressions and Markov chain Monte Carlo inference.
result Robust performance on various datasets, including single-atom catalysis.
The seemingly infinite diversity of the natural world arises from a relatively small set of coherent rules, such as the laws of physics or chemistry. We conjecture that these rules give rise to regularities that can be discovered through primarily unsupervised experiences and represented as abstract concepts. If such r…
Symbolic regression constructs smooth value functions for reinforcement learning.
problem Function approximators in reinforcement learning are black-box models with hyper-parameter tuning.
method Symbolic regression methods for constructing smooth value functions in the form of analytic expressions.
result Symbolic regression methods yield well-performing policies and are compact and mathematically tractable.
Transformer models can solve complex math problems with less data.
problem Solving complex symbolic mathematics problems with limited data.
method Pretrain transformer models on language translation tasks and fine-tune for symbolic math.
result Pretrained transformer models achieve comparable accuracy to state-of-the-art models with less data.
Deep learning finds mathematical equations from data.
problem Discovering underlying mathematical expressions from datasets.
method Uses a recurrent neural network to search for mathematical expressions and optimizes using a risk-seeking policy gradient.
result Outperforms existing methods in recovering exact symbolic expressions.
Zoetrope Genetic Programming improves symbolic regression performance.
problem Evolutionary symbolic regression for complex mathematical expressions.
method Zoetropic representation, repeated fusion operations, linear combination, crossover, mutation, selection.
result Zoetrope Genetic Programming achieves state-of-the-art performance and low computational time.
Active learning improves SR by proposing experiments in data-limited settings.
problem Efficiently gathering data for symbolic regression with physical constraints.
method Query by committee using the Pareto frontier of equations, with physical constraints.
result Reduces data required for SR and achieves state-of-the-art results.
Develops new approach to recover CR structures from their Levi foliations.
problem Recovering CR structures from their Levi foliations for nonregular symbols.
method Reduction to dynamical Legendrian contact structure on leaf space.
result New geometric interpretation of CR prolongation conditions.
DeepSIC learns to detect multiple symbols in MIMO systems without assuming a specific channel model.
problem Challenges in multiuser MIMO detection due to non-linear channels and lack of accurate channel state information.
method Integrates machine learning into iterative soft interference cancellation (SIC) algorithm to learn from limited training samples.
result Significantly outperforms conventional methods in linear and non-linear channels, even with CSI uncertainty.
MESSY estimation recovers symbolic density functions from samples using maximum entropy.
problem Estimating probability density functions from limited samples.
method Maximum-Entropy approach with gradient flow and symbolic regression.
result Efficiently finds optimal symbolic expressions for unknown distributions.
A hybrid algorithm combines optimization and enumeration for symbolic regression.
problem Finding any function from a set of operators without prior specification.
method Mixed-integer nonlinear optimization with explicit enumeration and constraints.
result The hybrid algorithm is competitive with state-of-the-art methods.
Unified tensor network formalism for combining neural and symbolic AI.
problem Combining neural and symbolic AI approaches remains a challenge.
method Introduces a tensor network formalism capturing sparsity principles.
result Unified treatment identifies tensor network contractions as a fundamental inference class.
Shape-constrained symbolic regression improves model extrapolation with prior knowledge.
problem Improving model extrapolation with prior knowledge in symbolic regression.
method Shape-constrained symbolic regression using evolutionary algorithms with interval arithmetic.
result Models with shape constraints have improved extrapolation but lower accuracy on test sets.
Efficient algorithm for identifying causal effects in linear models.
problem Determining causal effects from observational data under latent confounding.
method Symbolic computation and efficient algorithm for finding identifying formulas.
result Proves the existence of identifying formulas of a specified degree in quasi-polynomial time.
Study evaluates clustering methods for Google Trends data.
problem Clustering high-dimensional, noisy time series data.
method Symbolic Aggregate Approximation (SAX), Enhanced SAX (eSAX), and Topological Data Analysis (TDA).
result TDA provides more balanced and meaningful groupings than SAX and eSAX.
ABBA creates a new symbolic time series representation based on Brownian bridge.
problem Representing time series data in a compact, symbolic form.
method Adaptive polygonal chain approximation followed by mean-based clustering.
result ABBA outperforms other representations in preserving time series shape information.
ViterbiNet uses deep learning to detect symbols without channel info.
problem Symbol detection in digital receivers without channel state info.
method Integrates DNNs into Viterbi algorithm, leaving structure intact.
result Performance of ViterbiNet approaches CSI-based Viterbi, tracks dynamic channels.
We introduce the C++ library Wedge, based on GiNaC, for symbolic computations in differential geometry. We show how Wedge makes it possible to use the language C++ to perform such computations, and illustrate some advantages of this approach with explicit examples. In particular, we describe a short program to determin…
New algorithm improves interpretability in sequence classification.
problem Lack of human-independent interpretability metrics in sequence classification.
method Combines linear classifiers with background knowledge embeddings to create a new feature space.
result Preserves predictive power while delivering more interpretable models.